Joe Hockey has lashed out at “hysteria” over his comments that the fuel excise increase will have the biggest impact on high-income earners because “the poorest people either don’t have cars or actually don’t drive very far in many cases”.

The treasurer was seeking to reject claims low-income earners would bear the biggest burden from his budget, but Labor seized on the remark as evidence he was out of touch.

Hockey’s contribution to the fairness debate came after a meeting with the Palmer United party (PUP) leader, Clive Palmer, whose senators are crucial to the government’s hopes of passing contentious budget measures.

Palmer emerged from a separate meeting with the education minister, Christopher Pyne, on Wednesday saying he was “yet to be convinced” that deregulation of university fees had merit.

Hockey attempted to counter criticisms that the vulnerable, the young, the unemployed and those on pensions faced a disproportionate share of the budget pain.

“Well, everyone is being slugged and the fact is that someone on average weekly earnings is often paying all of their tax, so they work say a third of the year, to pay family benefits to someone on less than average weekly earnings,” Hockey told ABC radio on Wednesday.

“I don’t think that a cursory look at the budget is enough for people to understand what we’re really getting at. You have to look at the detail of what people actually receive now, and people are receiving tens of thousands of dollars in payments from other Australians.

“What we’re asking is for everyone to contribute, including higher-income people. Now, I’ll give you one example: the change to fuel excise. The people that actually pay the most are higher-income people, with an increase in fuel excise, and yet the Labor party and the Greens are opposing it. They say you’ve got to have wealthier people or middle-income people pay more.

“Well, change to the fuel excise does exactly that; the poorest people either don’t have cars or actually don’t drive very far in many cases. But they [Labor and the Greens] are opposing what is meant to be, according to the Treasury, a progressive tax.”

The government budgeted $2.2bn over four years from reintroducing twice-a-year indexation of fuel excise in line with the consumer price index, to be spent on road projects, but the proposal faces defeat in the Senate. The former prime minister John Howard froze fuel excise to counter community concern over rising fuel prices.

Despite Hockey’s argument that the fuel excise increase was “progressive”, welfare groups pointed out that the costs were a proportionately greater share of disposable income for the less wealthy.

An Australian parliamentary library research paper published in 2000 explained that “petrol and diesel excises are regressive in that people on low incomes pay a higher proportion of their incomes in the form of excise than people on high incomes, given the same level of fuel use”.

The opposition leader Bill Shorten, said Hockey had shown himself to be “remarkably arrogant and out of touch”.

“Are you serious, Joe Hockey? Are you really the caricature of the cigar-chomping, Foghorn Leghorn of Australian politics, where you’re saying that poor people don’t drive cars?” Shorten said in Perth.

“That’s particularly galling in WA where the Abbott government has cut half a billion in public transport projects, and yet Joe Hockey says they don’t drive cars, yet they don’t give them another alternative. It is almost though the treasurer believes that poor people should be sleeping in their cars, not driving their cars.”

The shadow treasurer, Chris Bowen, said Hockey’s “offensive and insulting comment” defied reality: “There are clearly high petrol costs for low-income people commuting between their suburban homes and capital cities around the country, not to mention low-income earners who rely on cars in regional and rural areas without any form of public transport alternative.”

Hockey’s office subsequently released analysis of the amounts different categories of households spent on fuel in a bid to counter the criticism.

“In terms of spending over the income distribution, average weekly expenditure on petrol in absolute terms increases with household income, from $16.36 at the lowest income quintile to $53.87 at the highest income quintile,” the analysis said.

The material, based on Australian Bureau of Statistics figures from 2009-10, did not include any analysis of fuel costs as a share of each household’s income.

It presented a separate graph showing that, based on census data, “households in relatively disadvantaged areas are less likely to own motor vehicles than those in relatively advantaged areas”.

In Perth for a meeting with the PUP senator Dio Wang, Hockey said there was “a great deal of hysteria around some of the initiatives in the budget”.

“For example the hysteria in relation to my comments this morning on car usage and fuel – my office is releasing the data that’s been provided to us and everyone can see that the fact is that there is a clear trend in Australia that the higher the household income the more fuel taxes are paid by that household. Simple as that, so therefore it’s good to get the facts out.”

Hockey said he stood by his comments: “I’m happy to lay down the facts and people can have a debate about them.”

In the earlier ABC interview, Hockey also defended the government’s plan to introduce a new $7 Medicare co-payment but confirmed the government was prepared to discuss possible exemptions for pensioners.

“You know, there is some irony in that pensioners pay over $360 for their pharmaceuticals each year, and when we ask for $70 to visit the doctor, if they have 10 visits, then the suggestion is somehow that’s unfair,” Hockey said.

Labor and the Greens oppose any form of Medicare co-payment. It is therefore doomed in the Senate unless the government can win over the PUP.